U.S. patent application number 15/446410 was filed with the patent office on 2018-09-06 for capillary network simulations based on a low-dimensional representation of porous media.
The applicant listed for this patent is International Business Machines Corporation. Invention is credited to Peter William Bryant, William Fernando Lopez Candela, Alexandre Ashade Lassance Cunha, Rodrigo Neuman Barros Ferreira, Mathias B. Steiner.
Application Number | 20180253514 15/446410 |
Document ID | / |
Family ID | 63355814 |
Filed Date | 2018-09-06 |
United States Patent
Application |
20180253514 |
Kind Code |
A1 |
Bryant; Peter William ; et
al. |
September 6, 2018 |
Capillary Network Simulations Based on a Low-Dimensional
Representation of Porous Media
Abstract
A method is provided including receiving data corresponding to a
three-dimensional physical representation of a porous rock sample;
calculating a low-dimensional representation of a pore network in
the porous rock sample based on the three-dimensional physical
representation; extracting one or more geometrical parameter from
the low-dimension representation; generating a capillary network
model of the porous rock sample based at least on the at least one
geometrical parameter for simulating fluid flow inside the porous
rock sample; and performing at least one simulation of a flow of
the fluid through the capillary network model of the porous rock
sample with a fluid additive to provide a predicted enhanced fluid
recovery efficiency.
Inventors: |
Bryant; Peter William; (Rio
De Janeiro, BR) ; Candela; William Fernando Lopez;
(Niteroi, BR) ; Cunha; Alexandre Ashade Lassance;
(Rio De Janeiro, BR) ; Ferreira; Rodrigo Neuman
Barros; (Rio De Janeiro, BR) ; Steiner; Mathias
B.; (Rio De Janeiro, BR) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
International Business Machines Corporation |
Armonk |
NY |
US |
|
|
Family ID: |
63355814 |
Appl. No.: |
15/446410 |
Filed: |
March 1, 2017 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06F 30/20 20200101;
G06F 2111/10 20200101 |
International
Class: |
G06F 17/50 20060101
G06F017/50 |
Claims
1. A method, comprising: receiving data corresponding to a
three-dimensional physical representation of a porous rock sample;
calculating a low-dimensional representation of a pore network in
the porous rock sample based on the three-dimensional physical
representation; extracting one or more geometrical parameter from
the low-dimension representation; generating a capillary network
model of the porous rock sample based at least on the at least one
geometrical parameter for simulating fluid flow inside the porous
rock sample; and performing at least one simulation of a flow of
fluid through the capillary network model of the porous rock sample
with a fluid additive to provide a predicted enhanced fluid
recovery efficiency.
2. The method of claim 1, wherein the low-dimensional
representation of the pore network is a centerline representation
that comprises a set of centerlines representing the pore
network.
3. The method of claim 2, wherein the centerline representation is
indicative of a spatial variation of a diameter, tortuosity,
geometry and connectivity of the pore network.
4. The method of claim 2, wherein extracting the at least one
geometrical parameter comprises generating a first list of values
for each centerline in the set, the first list comprising values
for at least one of the following centerline parameters: a
centerline diameter, a centerline length, centerline endpoints;
centerline direction; centerline azimuthal angle; centerline
tortuosity; centerline curvature; and centerline torsion.
5. The method of claim 4, wherein extracting the at least one
geometrical parameter further comprises generating a second list of
values defined for each pair of connected centerlines in the set of
centerlines, the second list comprising values for at least one of
the following centerline parameters: an angle between each pair of
connected centerlines: and a diameter variation between each pair
of connected centerlines.
6. The method of claim 5, wherein extracting the at least one
geometrical parameter further comprises calculating for the set of
centerlines at least one of: a total number of nodes at which
centerlines in the set connect to each other; a total number of
centerlines that are connected to an inlet and/or an outlet of a
given centerline in the set; a binary matrix depicting connections
between centerlines in the set; statistics corresponding to the
generated first lists and the generated second lists; and
two-dimensional plots relating every parameter in each of the first
lists to every parameter in the second list.
7. The method of claim 1, wherein performing at least one
simulation of capillary model comprises at least one of:
determining a simulation type comprising at least one of a
probabilistic simulation type that is time-independent, and a
dynamic simulation type that is time-dependent; determining a flow
regime where either inertial and kinetic forces are ignored in the
at least one simulation or inertial and kinetic forces are
considered in the at least one simulation; and determining an
interface type from a plurality of interface types, wherein the
plurality of interface types comprises at least one multi-phase
interface type.
8. The method of claim 7, wherein the interface type is selected
based on one or more of: wetting properties of the porous rock
sample; initial position of the fluid and initial fluxes, inlet
and/or outlet pressures, flow rates, and external forces; and
rheology properties and surface tension of the fluid.
9. The method of claim 7, wherein the interface type is selected by
a user via a user input.
10. An apparatus, comprising at least one processor; and at least
one memory including computer program code, the at least one memory
and the computer program code configured to, with the at least one
processor, cause the apparatus to at least: receive data
corresponding to a three-dimensional physical representation of a
porous rock sample; calculate a low-dimensional representation of a
pore network in the porous rock sample based on the
three-dimensional physical representation; extract one or more
geometrical parameter from the low-dimension representation;
generate a capillary network model of the porous rock sample based
at least on the at least one geometrical parameter for simulating
fluid flow inside the porous rock sample; and perform at least one
simulation of a flow of fluid through the capillary network model
of the porous rock sample with a fluid additive to provide a
predicted enhanced fluid recovery efficiency.
11. The apparatus of claim 10, wherein the low-dimensional
representation of the pore network is a centerline representation
that comprises a set of centerlines representing the pore
network.
12. The apparatus of claim 11, wherein the centerline
representation is indicative of a spatial variation of a diameter,
tortuosity, geometry and connectivity of the pore network.
13. The apparatus of claim 11, wherein extraction of the at least
one geometrical parameter comprises generating a first list of
values for each centerline in the set, the first list comprising
values for at least one of the following centerline parameters: a
centerline diameter, a centerline length, centerline endpoints;
centerline direction; centerline azimuthal angle; centerline
tortuosity; centerline curvature; and centerline torsion.
14. The apparatus of claim 13, wherein extraction of the at least
one geometrical parameter further comprises generating a second
list of values defined for each pair of connected centerlines in
the set of centerlines, the second list comprising values for at
least one of the following centerline parameters: an angle between
each pair of connected centerlines: and a diameter variation
between each pair of connected centerlines.
15. The apparatus of claim 14, wherein extraction of the at least
one geometrical parameter further comprises calculating for the set
of centerlines at least one of: a total number of nodes at which
centerlines in the set connect to each other; a total number of
centerlines that are connected to an inlet and/or an outlet of a
given centerline in the set; a binary matrix depicting connections
between centerlines in the set; statistics corresponding to the
generated first lists and the generated second lists; and
two-dimensional plots relating every parameter in each of the first
lists to every parameter in the second list.
16. The apparatus of claim 10, wherein performance of the at least
one simulation of capillary model comprises at least one of:
determination of a simulation type comprising at least one of a
probabilistic simulation type that is time-independent, and a
dynamic simulation type that is time-dependent; determination of a
flow regime where either inertial and kinetic forces are ignored in
the at least one simulation or inertial and kinetic forces are
considered in the at least one simulation; and determination of an
interface type from a plurality of interface types, wherein the
plurality of interface types comprises at least one multi-phase
interface type.
17. The apparatus of claim 16, wherein the interface type is
selected based on one or more of: wetting properties of the porous
rock sample; initial position of the fluid and initial fluxes,
inlet and/or outlet pressures, flow rates, and external forces; and
rheology properties and surface tension of the fluid.
18. The apparatus of claim 16, wherein the interface type is
selected by a user via a user input.
19. A computer program product for capillary network simulations,
the computer program product comprising a computer readable storage
medium having program instructions embodied therewith, the program
instructions executable by a device to cause the device to:
receiving data corresponding to a three-dimensional physical
representation of a porous rock sample; calculating a
low-dimensional representation of a pore network in the porous rock
sample based on the three-dimensional physical representation;
extracting one or more geometrical parameter from the low-dimension
representation; generating a capillary network model of the porous
rock sample based at least on the at least one geometrical
parameter for simulating fluid flow inside the porous rock sample;
and performing at least one simulation of a flow of fluid through
the capillary network model of the porous rock sample with a fluid
additive to provide a predicted enhanced fluid recovery
efficiency.
20. The computer program product of claim 19, wherein the
low-dimensional representation of the pore network is a centerline
representation that comprises a set of centerlines representing the
pore network, and wherein the centerline representation is
indicative of a spatial variation of a diameter, tortuosity,
geometry and connectivity of the pore network.
Description
TECHNICAL FIELD
[0001] The exemplary embodiments of this invention relate generally
to simulation methods, computer programs and apparatus and, more
specifically, to computer fluid flow simulations using a simplified
geometrical representation of porous network.
BACKGROUND
[0002] This section is intended to provide a background or context
to the invention disclosed below. The description herein may
include concepts that could be pursued, but are not necessarily
ones that have been previously conceived, implemented or described.
Therefore, unless otherwise explicitly indicated herein, what is
described in this section is not prior art to the description in
this application and is not admitted to be prior art by inclusion
in this section.
[0003] Fluid-fluid and fluid-solid interactions in digital rock
analysis (DRA) can be modeled in order to better predict enhanced
oil recovery (EOR) efficiency and to support decision-making in oil
recovery operations. One approach to such modeling is Pore Network
Modeling and its implementations focus on the connectivity of the
pore network. The complex geometry is reduced to a
"balls-and-sticks" representation. The geometry, morphology and,
most importantly, the surface aspects of it are often neglected,
giving rise to cruder models of the fluid flow. Fluid flow
properties are obtained using an electrical-analogue often without
dynamics, applying simpler heuristics and physical approximations
to describe the system.
BRIEF SUMMARY
[0004] This section is intended to include examples and is not
intended to be limiting.
[0005] In an example embodiment, a method is provided including
receiving data corresponding to a three-dimensional physical
representation of a porous rock sample; calculating a
low-dimensional representation of a pore network in the porous rock
sample based on the three-dimensional physical representation;
extracting one or more geometrical parameter from the low-dimension
representation; generating a capillary network model of the porous
rock sample based at least on the at least one geometrical
parameter for simulating fluid flow inside the porous rock sample;
and performing at least one simulation of a flow of the fluid
through the capillary network model of the porous rock sample with
a fluid additive to provide a predicted enhanced fluid recovery
efficiency.
[0006] In another example embodiment an apparatus is provided,
including at least one processor; and at least one memory including
computer program code, the at least one memory and the computer
program code configured to, with the at least one processor, cause
the apparatus to at least: receive data corresponding to a
three-dimensional physical representation of a porous rock sample;
calculate a low-dimensional representation of a pore network in the
porous rock sample based on the three-dimensional physical
representation; extract one or more geometrical parameter from the
low-dimension representation; generate a capillary network model of
the porous rock sample based at least on the at least one
geometrical parameter for simulating fluid flow inside the porous
rock sample; and perform at least one simulation of a flow of fluid
through the capillary network model of the porous rock sample with
a fluid additive to provide a predicted enhanced fluid recovery
efficiency.
[0007] In another example embodiment, a computer program product
for capillary network simulations, the computer program product
comprising a computer readable storage medium having program
instructions embodied therewith, the program instructions
executable by a device to cause the device to: receiving data
corresponding to a three-dimensional physical representation of a
porous rock sample; calculating a low-dimensional representation of
a pore network in the porous rock sample based on the
three-dimensional physical representation; extracting one or more
geometrical parameter from the low-dimension representation;
generating a capillary network model of the porous rock sample
based at least on the at least one geometrical parameter for
simulating fluid flow inside the porous rock sample; and performing
at least one simulation of a flow of fluid through the capillary
network model of the porous rock sample with a fluid additive to
provide a predicted enhanced fluid recovery efficiency.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] In the attached Drawing Figures:
[0009] FIG. 1 illustrates a non-limiting example of a simulator and
simulation workflow in accordance with example embodiments.
[0010] FIG. 2 is a flow chart for computing centerlines in
accordance with example embodiments;
[0011] FIG. 3 is a flow chart for extracting centerline parameters
in accordance with example embodiments;
[0012] FIG. 4 is a flow chart for simulating a capillary model in
accordance with example embodiments;
[0013] FIGS. 5A and 5B is a non-limiting example of a capillary
network and the corresponding system of equations used to find
nodal pressures in accordance with example embodiments;
[0014] FIG. 6 is an example of a graphical user interface
presentation to a user of the simulator shown in FIG. 1;
[0015] FIG. 7 shows a comparison for different representations of a
porous rock sample;
[0016] FIG. 8 is an example of a block diagram of the simulator
shown in FIG. 1; and
[0017] FIG. 9 is a logic flow diagram for capillary network
simulations based on a low-dimensional representation of porous
media, and illustrates the operation of an exemplary method, a
result of execution of computer program instructions embodied on a
computer readable memory, functions performed by logic implemented
in hardware, and/or interconnected means for performing functions
in accordance with exemplary embodiments.
DETAILED DESCRIPTION
[0018] The word "exemplary" is used herein to mean "serving as an
example, instance, or illustration." Any embodiment described
herein as "exemplary" is not necessarily to be construed as
preferred or advantageous over other embodiments. All of the
embodiments described in this Detailed Description are exemplary
embodiments provided to enable persons skilled in the art to make
or use the invention and not to limit the scope of the invention
which is defined by the claims.
[0019] An alphabetically arranged list of abbreviations and
associated definitions that occur in the description of the
invention is provided below for the convenience of the reader.
[0020] DRA digital rock analysis [0021] EOR enhanced oil recovery
[0022] MPS multi-point statistics [0023] MSPS multiscale
percolation system
[0024] As employed herein a voxel can be considered as a `volume
pixel` that is one element of an array of elements of volume.
[0025] The exemplary embodiments herein describe techniques for
capillary network simulations based on a low-dimensional
representation of porous media.
[0026] Relevant teachings have addressed the concept of "Pore
Network Model" (PNM), which describes a complex porous network in
terms of a dichotomist pores-and-throats (or balls-and-sticks)
approximation; explored centerline extraction algorithms to obtain
a one-dimensional representation of simple, often tubular,
geometries of medical interest; described centerline extraction
algorithms for generation of one-dimensional representations of
complex porous media; and have explored estimating flow properties
of a porous medium phenomenological relationships between capillary
diameter, capillary pressure and permeability.
[0027] However, each of these teachings include, for example, one
or more of the following characteristics: inaccurately describe the
geometrical and spatial variation of confining diameter; fail to
produce a one-dimensional capillary representation of the rock; do
not describe the use of capillary flow models or any pore-scale
flow model; cannot predict flow properties from first-principles
representation; employ 2D images (from profilometry) to generate 3D
samples using MPS, instead of starting directly from 3D images;
failure to address computation of centerline representation of 3D
geometries; failure to address centerline extraction from
non-tubular source geometries; do not consider the planarization of
a capillary geometry suitable for manufacturing representative flow
chips; do not prescribe a dynamic, physics-based simulation; do not
employ a continuous spatially-dependent description of the diameter
variation along the pore channels; and do not allow the usage of
different physical models including, for instance, nanoscale
physical effects.
[0028] The exemplary embodiments encompass the use of a system
(including sensors, hardware and software) that utilizes capillary
network modeling of fluid flow to determine flow properties for
recovery enhancers such as chemicals, polymers, nanoparticles,
emulsions, gas bubbles, etc., when such recovery enhancers are
added to the system.
[0029] A number of advantages can be gained by using capillary
network modeling to help better describe fluid flow in a porous
media. One such advantage is providing a computationally efficient
process for simulations due to the simplified spatial
representation of the porous rock, without sacrificing the
nanoscopic physical detail required for obtaining accurate results.
This simplified process enables faster turnaround time for
simulations to support decision-making in large oil and gas
operations.
[0030] The embodiments of the simulator in accordance with this
invention beneficially enable a user to screen a set of potential
additives for use in the field to enhance oil recovery, without
requiring expensive and time consuming field trials to be
conducted.
[0031] Reference can now be made to FIG. 1 for showing a
non-limiting example of a simulator 10 and a simulation
process/method workflow in accordance with embodiments of this
invention. The rock sample, R, represents a physical input to the
simulator. The blocks S.sub.1, S.sub.n, S.sub.N are representative
of various data sources that are employed to perform
characterization on R. An exemplary instance of sensor
characterization is a three-dimensional physical representation of
a porous medium, such as the one obtained by segmenting a Computed
Tomography (CT) of a reservoir rock with micro-/nanometer
resolution. These blocks, in addition to the blocks labeled 1A and
1B, may be characterized as being data generation and/or data
integration functions. The blocks labeled 1L and 1M may be
characterized as being visualization functions that can use a
graphical user interface (GUI) to display results to a user. The
remaining blocks 1C-1G and 1H-1K may be characterized as being
computation/algorithmic functions.
[0032] In general, the various blocks of the simulator 10 that are
shown in FIG. 1 can be implemented in whole or in part as discrete
logic functions/engines, or they can be implemented in whole or in
part by program code modules/subroutines/algorithms (computer
program code), or they can be implemented as a combination of
discrete logic functions/engines and computer program code.
[0033] The simulation workflow begins by populating an EOR database
1B from block 1A with physical characterizations of fluids and
solids (rocks and dispersed particles). Block 1A receives the
outputs of the S.sub.1, S.sub.n, S.sub.N and supplies these as the
physical characterizations of fluids and solids to the EOR database
1B. These physical characterizations can include but are not
limited to material data and flow properties data. This data may
originate from the array of sources {S.sub.n} such as sensors,
experimental tools, ab initio simulations, phenomenology and/or
libraries. Rock characterization input data to the EOR database 1B
provides at least geometrical information on a pore network of
interest while the solid characterization input data to the EOR
database 1B provides physical information regarding, for example,
the wetting, chemistry, material, mechanical, spectroscopical,
etc., properties of the solids involved in the simulation (rocks or
suspended particles). Fluid characterization input data to the EOR
database 1B can be represented as a list of fluid properties such
as, but not limited to, density, viscosity, surface tension, line
tension, molecular composition, structural factors and/or
compressibility. The EOR database 1B is then loaded into the
simulator 10 by data loading block 1C and consumed by the simulator
10 in order to begin processing the stored information.
[0034] The rock characterization input of block 1A may arise from
various experimental and/or simulated sources. A three dimensional
(3D) tomographic image, either obtained experimentally or generated
numerically from a set of two dimensional (2D) images, can be read
by the simulator 10. The 3D tomographic image is comprised of a
collection of voxels (volume pixels), each representing a region of
the sample of interest at a certain length scale. The voxel size
(resolution) determines the scale at which the physics of the
fluid-solid interaction should be captured by the simulator 10.
[0035] Experimental techniques such as, but not limited to, X-ray
computed micro-tomography/nano-tomography, synchrotron computed
micro-tomography/nano-tomography, dual-energy computed
micro-tomography/nano-tomography, focused ion beam tomography,
electron tomography, 3D atom probe, etc., may be used to measure
the rock structure and to store the structural geometry in a data
file. In computerized tomography, the voxels typically hold a
grayscale integer value (from 0 to 255 in 8-bit notation or 0 to
65535 in 16-bit notation) that is representative of the density and
atomic number of the sample at that point. Denser regions are
associated with the rock itself while lighter regions are
associated with the pore space within the rock.
[0036] Certain numerical techniques, such as the MPS or the MSPS,
can also be used to create 3D pseudo-cores suitable for use in the
simulator 10 from a set of 2D images. Techniques for accomplishing
this are described in, for example, Zhang et al., U.S. Pat. No.
8,725,477 B2, Hurley et al., U.S. Pat. No. 8,908,925 B2 and Hurley
et al., US 20120221306 A1, as well as in Daian et al., Journal of
Petroleum Science and Engineering 42 (2004) 15-28, Fernandes et
al., Physical Review E 54, 1734 (1996) and Liang et al., Journal of
Petroleum Science and Engineering 21, Issues 3-4, November 1998,
Pages 273-283. Such 2D images can be obtained from experimental
techniques such as scanning electron microscopy, scanning probe
microscopy, atomic force microscopy and laser scanning fluorescence
microscopy. Alternatively, any ad hoc 3D porous geometry, such as a
close packing of spheres, can also be used as input. In addition,
rock input data can be loaded from a library that may be
proprietary or open, such as ROCKETH Group,
http://www.rockphysics.ethz.ch/, Imperial College Department of
Earth Science and Engineering, and/or Digital Rock Portal @
University of Texas.
[0037] The solid characterization input of block 1A conveys
additional physical information such as chemistry, material,
mechanics, spectroscopy, etc., other than the purely geometrical
information that can be assigned to the solid voxels in order to
augment the physical meaning attributed to them.
[0038] The operation of the simulator 10 can be enhanced by
assigning additional information to the voxels such as, but not
limited to, chemical composition, molecular termination, free
energy, surface charge and philicity or phobicity towards a certain
fluid. The solid characterization can be assumed to include as well
the characterization of any solid particles that are to be
dispersed in the embedding fluids.
[0039] The additional physical information of the solid
characterization input is preferably representative of the solid
properties at the same scale (voxel) as the geometric detail of the
rock characterization input of block 1A is provided. Alternatively,
if only information from a different scale is present, the required
voxel-scale analog can be complemented by interpolation,
extrapolation or by additional assumptions and calculations. The
possible sources of the additional physical information are many
and typically are ultimately defined by the length scale
corresponding to the voxel size.
[0040] For nanometer-sized voxels it is possible to use either
experimental nanoscience techniques (such as scanning probe or
electron microscopy, hyperspectral imaging, confocal laser scanning
microscopy, etc.) or atomic-scale or molecular-scale computer
simulations (such as atomistic molecular dynamics, coarse-grained
molecular dynamics, Monte Carlo, etc.) For micrometer-sized voxels
it is possible to use experimental mesoscale techniques (such as
profilometry, petrography, optical microscopy, mercury porosimetry,
etc.) or mesoscale numerical techniques (such as the LBM,
dissipative particle dynamics, smoothed particle dynamics, etc.) as
is deemed most appropriate.
[0041] Alternatively, and for any length scale of interest, it is
possible to resort to libraries and published results in the
literature to populate the EOR database 1B with the physical
properties required as inputs to the simulator 10. In addition, in
a case where such additional information is not available an ad hoc
value for the required physical property can be assigned to the
voxels by the user.
[0042] After loading the EOR database 1B the process flow continues
to execute block 1D where the geometrical properties of the rock
can be determined by the application. The rock sample geometry
determination of block 1D may involve image processing algorithms
such as, but not limited to, noise-removal filters, image
segmentation, image labeling and pixel statistics as well as 3D
visualization of the geometry. The geometry determination of block
1D may also employ data from the solid characterization input of
block 1A by correlating, for example, spectroscopy data (material)
and tomography data (grayscale level) in order to enhance image
segmentation algorithms. One goal of the geometry determination of
block 1D is to segment the sample image into first voxels
corresponding to "rock" and second voxels corresponding to "pores".
A binary segmentation process can be employed in this regard.
[0043] At block 1E, the computation of centerlines is performed.
Referring also to FIG. 2, this figure is an example flow chart for
performing the computation of centerlines. At block 200, a
hierarchical representation of the pore space is built.
Non-limiting suitable representations include any geometrical
entity that corresponds to a subset of pore space voxels annotated
with a certain measure of their distance to the boundary, such as:
[0044] Distance Map (see, e.g., Kimmel, Ron, Nahum Kiryati, and
Alfred M. Bruckstein. "Sub-pixel distance maps and weighted
distance transforms." Journal of Mathematical Imaging and Vision
6.2-3 (1996): 223-233.), [0045] Line/Straight Skeleton (see, e.g.,
Aichholzer, Oswin, and Franz Aurenhammer. "Straight skeletons for
general polygonal figures in the plane." International Computing
and Combinatorics Conference. Springer Berlin Heidelberg, 1996.);
[0046] Multi-Scale Skeleton (see, e.g., Falcao, Alexandre X.,
Luciano da Fontoura Costa, and B. S. Da Cunha. "Multiscale
skeletons by image foresting transform and its application to
neuromorphometry." Pattern recognition 35.7 (2002): 1571-1582.);
and [0047] Medial Axis see (see, e.g., Amenta, Nina, Sunghee Choi,
and Ravi Krishna Kolluri. "The power crust, unions of balls, and
the medial axis transform." Computational Geometry 19.2 (2001):
127-153.).
[0048] Any combination of the above representations could also be
used. The hierarchical representation need not be linear, and it
may have planar patches. Suitable algorithms for obtaining such
representations include: [0049] Thinning (see, e.g., Cheriet,
Mohamed, et al. Character recognition systems: a guide for students
and practitioners. John Wiley & Sons, 2007); [0050] Voronoi
Diagrams (see, e.g., Aurenhammer, Franz. "Voronoi diagrams--a
survey of a fundamental geometric data structure." ACM Computing
Surveys (C SUR) 23.3 (1991): 345-405.); [0051] Image Foresting
Transform (see, e.g., Falcao, Alexandre X., Jorge Stolfi, and
Roberto de Alencar Lotufo. "The image foresting transform: Theory,
algorithms, and applications." IEEE Transactions on Pattern
Analysis and Machine Intelligence 26.1 (2004): 19-29.); [0052]
Medial Axis Transformation (see, e.g., Sherbrooke, Evan C.,
Nicholas M. Patrikalakis, and Erik Brisson. "An algorithm for the
medial axis transform of 3D polyhedral solids." IEEE transactions
on visualization and computer graphics 2.1 (1996): 44-61.); [0053]
Euclidean Distance Transform (see, e.g., Breu, Heinz, et al.
"Linear time Euclidean distance transform algorithms." IEEE
Transactions on Pattern Analysis and Machine Intelligence 17.5
(1995): 529-533.); and/or [0054] a combination of the above.
[0055] At block 202, voxels are selected, from the hierarchical
representation built at block 200, at the edges of the original
image (external faces of the .mu.CT cube) corresponding to the
entrance/exit of individual pores. According to an embodiment, the
voxel selected is the most central voxel at the entrance/exit of an
individual pore, a task for which the centrality-related voxel
annotations might be useful. The larger the distance to the
boundary, the larger the centrality of a voxel.
[0056] At block 204, a graph is built starting from the
hierarchical representation where the voxels are vertices and
neighborhood relationships are edges.
[0057] At 206, a cost function is defined. In particular, a cost is
attributed for moving along an edge from one voxel to another,
i.e., the weight of an edge. The cost associated to moving along an
edge towards a specific voxel is inversely proportional to its
centrality. Suitable choices for a cost function include, the
inverse distance (when using Distance Map), the inverse skeleton
level (when using Multi-Scale Skeleton) and/or simply the linear
distance between voxels (when using Medial Axis or Line
Skeleton).
[0058] At 208, the "shortest path" is determined (that with the
lower cost) from all inlet voxels to all outlet voxels in the graph
from block 204 using the cost function from block 206. Any suitable
shortest path algorithm may be used, including but not limited to:
[0059] Single-Source Shortest Path algorithms (see, e.g., E. W.
Dijkstra. A Note on Two Problems in Connexion with Graphs. In
Numerische Mathematik 1, 1959; Bellman, Richard. "On a routing
problem." Quarterly of applied mathematics (1958): 87-90; Garbow,
Harold N. "Scaling algorithms for network problems." Journal of
Computer and System Sciences 31.2 (1985): 148-168; and Thorup,
Mikkel. "Integer priority queues with decrease key in constant time
and the single source shortest paths problem." Proceedings of the
thirty-fifth annual ACM symposium on Theory of computing. ACM,
2003); and [0060] All-Pairs Shortest Path algorithms (see, e.g.,
Floyd, Robert W. "Algorithm 97: shortest path." Communications of
the ACM5.6 (1962): 345; Johnson, Donald B. "Efficient algorithms
for shortest paths in sparse networks." Journal of the ACM (JACM)
24.1 (1977): 1-13; Williams, Ryan. "Faster all-pairs shortest paths
via circuit complexity." Proceedings of the 46th Annual ACM
Symposium on Theory of Computing. ACM, 2014; Pettie, Seth. "A new
approach to all-pairs shortest paths on real-weighted graphs."
Theoretical Computer Science 312.1 (2004): 47-74; and Hagerup,
Torben. "Improved shortest paths on the word RAM." International
Colloquium on Automata, Languages, and Programming. Springer Berlin
Heidelberg, 2000.)
[0061] The result if block 208 is a set of one-voxel-wide paths
from every inlet voxel to every outlet voxel.
[0062] At 210, all the shortest paths from block 208 are combined
with the distance of each voxel to the nearest boundary from the
hierarchical representation from block 200. Eventual overlaps
between centerlines are removed. The result is a tubular
representation of the pore space that takes into account the
spatial variation of the diameter, tortuosity, geometry and
connectivity.
[0063] Referring again to FIG. 1, block IF of the simulator 10
determines the mechanical properties of the rock. The mechanical
determination of block IF can include the calculation of the
mechanical and seismic properties of the rock such as, but not
limited to, shear and bulk moduli, formation factor, elasticity,
compressional velocity, shear velocity and electrical resistivity,
which can also benefit seismic modeling simulators. Significantly,
the mechanical determination process of block IF may also apply
reservoir-like conditions of pressure and temperature to deform the
rock structure towards its reality in the oil field. As a result,
the input to the flow simulation can be even more representative of
the actual, real rock sample.
[0064] At block 1G centerline parameters are extracted using the
computed centerlines from block 1E. Referring also to FIG. 3, this
figure shows a flow chart for computing the centerlines of block
1G. At block 300, a list of centerline properties defined for each
individual centerline is calculated. In particular, the
single-centerline properties include one or more of the following:
[0065] Centerline diameter, i.e., the diameter associated with each
centerline. The centerline diameter is useful for calculating flow
rates and capillary pressures. [0066] Centerline length, i.e., the
length associated to each centerline. The centerline length is
useful for calculating pressure differences and hydrostatic
effects. [0067] Centerline endpoints, i.e., the positions of
starting and end points of each centerline.
[0068] The centerline endpoints are useful for calculating
connectivity and direction. [0069] Centerline direction, i.e., the
vector connecting endpoints of each centerline. The centerline
direction is useful for calculating tortuosity, connectivity and
gravitational effects. [0070] Centerline azimuthal angle, i.e., the
angle between centerline direction and vertical direction. The
centerline azimuth angle is useful for calculating gravitational
effects. [0071] Tortuosity, i.e., the measure of how much each
centerline differs from a straight line. The tortuosity is useful
for upscaling. [0072] Curvature, i.e., the measure of each
centerline curvature radius. The curvature is useful for
calculating inertial effects. [0073] Torsion, i.e., the measure of
how sharply each a centerline is twisted out of its plane of
curvature. The torsion is useful for calculating inertial
effects.
[0074] At block 302, a list of centerline properties is calculated
and generated that are defined for a pair of connected centerlines.
The list of centerline properties for the pair of connected
centerlines include one or more of the following: [0075] Angle
between centerlines, i.e., angle between two connected centerlines.
The angle between the centerlines is useful for calculating
tortuosity. [0076] Diameter variation, i.e., a difference in
diameter between two connected centerlines. The diameter variation
is useful for calculating inertial and capillary effects.
[0077] At block 304, correlation plots for pairs of centerline
properties are calculated and statistics are calculated and
correlation plots are generated for pairs of properties that are
defined for all of the centerlines. Block 304 may output one or
more of the following: [0078] Node count: A number of nodes at
which centerlines connect to each other. The node count is useful
for estimating computational complexity. [0079] Fan in/Fan out:
number of centerlines connected to the inlet/outlets of a given
centerline. Useful for estimating overall connectivity. [0080]
Connection matrix: binary matrix depicting the connection between
centerlines. Useful for building the physical model. [0081]
Statistics: histogram, mean, min, max of each parameter in the
one-centerline and two-centerline lists. Useful for upscaling.
[0082] Correlations: 2D-plots relating every one-centerline and
two-centerline property to every other property of the same type,
such as plotting the diameter of a centerline versus its length for
all centerlines, or a first two-centerline property (e.g. angle)
versus a second two-centerline property (e.g. diameter variation),
for every pair of centerlines. These correlations are useful for
upscaling.
[0083] Referring again to FIG. 1, at block 1H the various outputs
of block 1D-1G may be validated against known experimental results
by the experimental validation block 1H. The experimental
validation process of block 1H can include, as non-limiting
examples, a comparison of porosity, density, bulk and shear moduli
and sound wave speeds to known experimental results.
[0084] For example, if the computed porosity of the digital rock
sample does not match an experimentally determined porosity that
was obtained by mercury porosimetry experiments one may be required
to redo the micro-tomography using better spatial resolution and/or
signal-to-noise ratios. Conversely, if the computed density does
not match the experimental value one may need to recompile the list
of constituent minerals and perform multi-level image segmentation
to account for different mineral (solid) phases. As such, an
iterative path (the No branch from block 1H) can be established
and, at each iteration loop, the EOR database 1B can be augmented
with additional, improved information that ultimately leads to an
acceptable low-dimensional representation of the pore network of
the rock at block 1G that terminates the iterative loop.
[0085] After the accuracy checks have been performed and the
low-dimensional representation of the pore network has been
experimentally validated at block 1H, control passes to block 11
where a list of target figures-of-merit is compiled, both for the
solid (rock) and fluid physical properties. The values of such
properties may, preferentially, be provided either by experiments
or by ab initio atomic-scale/molecular-scale calculations, where
the property values are preferably sensitive to nanoscale
phenomena. An exemplary and non-exhaustive list of target
nanoscale-aware figures-of-merit may include one or more of: (a)
contact angles or appropriate measures of the rock's wettability
with respect to one or more fluids; (b) fluid properties such as,
but not limited to, density, viscosity, surface tension, line
tension and compressibility; and (c) permeability with respect to
single-phase and two-phase flow of simple fluids such as water
and/or oil.
[0086] Relatedly, a concept of "full-sample dimensions" pertains to
a length scale at which the figures-of-merit are defined. The
figures-of-merit can be defined at a length scale that corresponds
to the entire digital rock sample (for example, a computed
micro-tomography scan), hence "full-sample dimensions". Note,
however, that certain properties such as, for example, permeability
cannot be defined at sub-micron scales. The figures-of-merit,
although defined for "full-sample dimensions", can be highly
sensitive to nanoscale phenomena, and it is in this sense that the
model can be calibrated. In this case then it is desirable to tune
the nanoscale interactions and observe their effect upon larger
length scale properties such as, for example, the permeability of
the entire porous rock sample.
[0087] After the list of figures-of-merit is compiled at block 1I
the operation of the simulator 10 progresses to blocks 1J, 1K and
1L. It can be noted that recursions are possible between certain of
these blocks, in particular between the flow model calibration
block 1J and the figures-of-merit compilation block 11, and between
the flow properties determination block 1L and the flow model
calibration block 1J (the line labeled "change additive").
[0088] Basically the portion of the simulator 10 represented by the
blocks 1J, 1K and 1L involves the use of computational fluid
dynamics algorithms such as, but not limited to, physics-based flow
models including, for example, the Capillary Network Model. The
geometrical and centerline data derived in blocks 1D, 1E (and 1F)
may also be used as input to the fluid dynamics simulations.
[0089] In accordance with the selected flow model, the flow model
calibration block 1J is operated to tune the (often unphysical)
flow model parameters so that the nanoscale-aware figures-of-merit
determined and enumerated at block 11 are matched as closely as
possible. As was noted above, one exemplary figure-of-merit might
be, for example, the water-oil contact angle on a given
surface.
[0090] Note that certain additives such as, but not limited to,
chemicals, polymers, nanoparticles, emulsions and gas bubbles can
have an effect of changing the contact angle of an oil droplet on
the rock surface thereby leading to a lower wettability and a
higher oil recovery rate. Such a modification to the
figure-of-merit (contact angle) is also preferably captured by the
flow model calibration block 1J.
[0091] When all of the model parameters are calibrated with respect
to their respective target figures-of-merit, the flow model is
ready to provide predictive results. The iterative loop represented
by the change additive arrow between the flow properties
determination block 1L and the flow model calibration block 1J can
be implemented simply by taking available candidate additives from
a predefined list of additives, or by using an additive design
methodology that tailors and optimizes the additive to maximize EOR
efficiency.
[0092] Reoffering also to FIG. 4, this figure shows a flow chart
for simulating the flow simulation of the capillary model at block
1K. In accordance with example embodiments.
[0093] At block 400, a desired simulation type is selected, e.g.
via a user input. Options for the simulation type include dynamic
and probabilistic simulation types. The probabilistic simulation
type is based on a time-independent model where sweep efficiency
and/or saturation distribution is calculated. As an example, a
probabilistic simulation type may include quasi-static simulations
[two-phase systems] in which time is ignored and capillaries fill
one-at-a-time depending on pressure, in a probabilistic fashion.
Generally a probabilistic simulation type will have a lower
computational cost. Dynamic simulation types are based on a
time-dependent model, where velocity and/or pressure fields may be
calculated. For instance, dynamic simulation types may include one-
or two-phase models where parameters such as interface positions,
flow rates, and pressures are functions of time, with a higher
computational cost for multiple phase systems.
[0094] As a non-limiting example, the following document provides a
review of dynamic and probabilistic methods implemented in Pore
Network Models: Blunt, Martin J., et al. "Detailed physics,
predictive capabilities and macroscopic consequences for
pore-network models of multiphase flow." Advances in Water
Resources 25.8 (2002): 1069-1089. However, it is noted that Pore
Network Models differ from capillary models as Pore Network Models
do not consider the continuous spatial variation of the pore
channel diameters.
[0095] At block 402, a flow regime is chosen to calculate the main
forces in the capillary. The choice in flow regime may include, for
example, stokes and quasi-static regime which neglects inertial and
kinetic forces. Alternatively, the choice of flow regime may be a
Laminar regime, where inertial and kinetic forces are considered.
Depending on the choice of flow regime at block 402, forces, such
as viscous, inertial, kinetic, hydrostatic forces, may be
calculated.
[0096] At block 404, an interface type is chosen. The choice of
interface type affects the accuracy and computational cost (e.g.,
see, H. T. Xue, Z. N. Fang, Y. Yang, J. P. Huang, L. W. Zhou.
Contact angle determined by spontaneous dynamic capillary rises
with hydrostatic effects: Experiment and theory. Chemical Physics
Letters 432 (2006) 326-330). In single-phase flow simulations there
is no interface to be accounted for. For multi-phase flows an
interface type may be selected, such as a static interface, a
simplified interface, or a dynamic interface. A static interface
type is associated with a lower accuracy, but also requires a lower
computational cost. A simplified interface is an equilibrated model
and is adequate for Stokes regime. A dynamic interface provides
high accuracy and also high computational cost. A dynamic interface
is adequate for a laminar regime for example. The choice of
interface type may also depend on availability of wetting data for
specific systems. Wetting properties are typically parameterized by
a three-phase contact angle, though parameterizations can vary
depending on the physical model selected. For example, the wetting
character of a fluid "A" with respect to a solid surface "S" in the
presence of a second fluid "B" may be represented in terms of the
three-phase (A-B-S) contact angle. Other metrics of wettability are
also possible, such as the adsorption energy density and the
contact-area-to-volume-ratio.
[0097] At block 406, a physical model is selected that will be used
to represent capillary flow. In some examples, the simulator 10 may
automatically (i.e. without user input) select a best model
considering one or more of the following: simulation type; flow
regime; interface type; wetting properties (e.g. relationship
between dynamic parameters to deduce the wetting parameters: P-Q,
V-contact angle, X-t); boundary conditions (inlet/outlet pressures
and flow rates, external forces); fluid properties (e.g. rheology
properties and surface tension), and initial conditions (e.g.
initial fluid positions, initial fluxes) provided by the user. In
other examples, the physical model may be selected manually by a
user, e.g., via a user input. Some non-limiting examples of
physical models include: Darcy, Poiseuille, Leonard-Washburn,
Molecular Kinetic model (see, e.g., Whitaker, Stephen. "Flow in
porous media I: A theoretical derivation of Darcy's law." Transport
in porous media 1.1 (1986): 3-25; Washburn, Edward W. "The dynamics
of capillary flow." Physical review 17.3 (1921): 273.atik 1.1
(1959): 269-271; and Blake, Terence D. "The physics of moving
wetting lines." Journal of Colloid and Interface Science 299.1
(2006): 1-13).
[0098] At block 408, a system of equations is built upon the
centerline structure of the porous rock sample. The system will
depend on pore centerline properties extracted in block 1G of FIG.
1, and also on the simulation type (dynamic or probabilistic),
physical model, and conservation equations. The system of equations
may solve for nodal pressures or fluid flow rates within the
capillary network (see, e.g., Blunt, Martin J., et al. "Detailed
physics, predictive capabilities and macroscopic consequences for
pore-network models of multiphase flow." Advances in Water
Resources 25.8 (2002): 1069-1089; and Nordhaug, Hans Fredrik, M.
Celia, and Helge K. Dahle. "A pore network model for calculation of
interfacial velocities." Advances in Water Resources 26.10 (2003):
1061-1074). A non-limiting example of a capillary network and the
corresponding system of equations used to find nodal pressures is
shown at FIGS. 5A and 5B. The capillary network shown in FIG. 5A is
generated based on pore centerline data. In FIG. 5B, P.sub.in
corresponds to pressures at the inlets of the capillary network in
FIG. 5A, and P.sub.out corresponds to the pressures at the outlets
of the capillary network in FIG. 5A.
[0099] At block 410, a hydrodynamics simulation includes resolving
pressures and/or flow rates, iterating to find the pressures at
nodes or flow through the capillaries, iterating through time or
pressure changes as necessary (such as for two-phase, probabilistic
or dynamic for example), and extracting the desired results. The
nodal pressures may be determined using analytical (Gauss-Jordan
elimination) or numerical methods (Runge-Kutta method) (see, e.g.,
Aker, Maloy and Hansen. A two-dimensional network simulator for
two-phase flow in porous media. IKU Petroleum Research, N-7034
Trondheim, Norway; and Beamount, Bodiguel and Colin. Drainage in
two-dimensional porous media with polymer solutions. Soft Matter,
2013, 9, 10174). The desired physical quantities may include
permeability tensors, drainage curves, oil left in place, and flow
rates for example.
[0100] Returning to FIG. 1, the final goal of this process is the
determination of flow properties at block 1L. The flow properties
can contain three-dimensional fields (scalar, vector or tensor)
representing spatially-dependent physical data in the rock sample
such as, but not limited to, flow velocity, pressure and density,
as well as overall physical properties (scalar, vector or tensor)
that quantitatively characterize the fluid flow and the oil
recovery in the porous rock sample such as, but not limited to,
absolute and relative permeability tensors, oil sweep efficiency
and capillary pressure.
[0101] The arrow labeled "correlation" between the extract
centerline parameters process of block 1G and the flow properties
determination process of block 1L indicates an ability to verify
that the determined flow properties are compatible with the
previously determined geometrical, morphological and mechanical
properties of the rock.
[0102] The EOR efficiency prediction block 1M can be implemented as
a visualization process using a GUI, an example output of which is
shown in FIG. 6 for three selected additives (A, B and C) and with
no additive. This process of the simulator 10 enables a
quantification to be made of the effect of an additive or additives
on the flow properties. Once all candidate additives have been
tested, their EOR efficiency with respect to, for example, a simple
water-flooding (without additives) and to one another can be
quantified and ranked, allowing for the selection of the best
candidate EOR approach, while considering also, for example,
cost-effectiveness criteria. The GUI can be useful to display the
simulator 10 results for different candidate EOR additives to aid
in determining an optimum EOR approach. In the illustrated example
three additives (and no additive) are characterized for EOR
efficiency vs. concentration and for EOR efficiency vs. cost and
additive C is shown to provide the best approach.
[0103] The various buttons displayed on the GUI can be used to
initiate the various simulator blocks/processes (e.g., load data
1C, geometry determination 1D, compute centerlines 1E, etc.) as
described above with reference to FIG. 1.
[0104] An output from the EOR efficiency prediction block 1M,
representing a result of the simulation workflow including EOR
efficiencies for each tested additive and other information, can be
fed back to the EOR database 1B. By augmenting the EOR database 1B
with the information descriptive of EOR efficiency it becomes
possible to build a knowledge base that can be later accessed by,
as one non-limiting example, a cognitive processing system for
providing insights into EOR strategies. The EOR database 1B can
contain, for example, both structured and unstructured data related
to the inputs and outputs of all system processes, as well as
external information (with respect to the system) that can,
however, be correlated to the system data. Non-limiting examples of
such data can include bulk scalar (porosity), vector (average flow
velocity vector) or tensor (permeability) variables,
spatially-dependent scalar (density), vector (flow velocity) or
tensor (stiffness) fields as well as images (graphs), texts
(reports) and various tables of interest (e.g., cost of
additives).
[0105] An advantage of the techniques described above is providing
a computationally efficient process for simulations due to the
simplified spatial representation of the porous rock, without
sacrificing the nanoscopic physical detail required for obtaining
accurate results. FIG. 7 shows a comparison of different
representation of a porous rock sample. The left image is a binary
CT representation of the rock sample, the middle image is a pore
space model representation of the rock sample, and the right image
is a centerline representation of a rock sample. Image captions
indicate the number, both absolute and as a percentage of the size
of the binary CT representation, of voxels required for each
representation. As shown in FIG. 7, the centerlines representation
has significantly fewer voxels, and which allows for more efficient
processing.
[0106] FIG. 8 is an example of a block diagram of the simulator 10
shown in FIG. 1. The simulator 10 includes at least one
controller/data processor 102 connected with at least one memory
104 that stores software (SW) 106. The software 106 can include
those programs that are desirable to run to perform the
determinations of the geometrical properties, mechanical properties
of the rock (blocks 1D, 1F) and the computation of the centerlines
and extraction of the centerline parameter (blocks 1E and 1G), the
experimental validation operation of block 1H, the compilation of
the list of figures-of-merit of block 11, the flow model
calibration of block 1J, the flow simulation for the capillary mode
of block 1K, the flow properties determination of block 1L and the
EOR efficiency prediction performed by block 1M. Bi-directionally
connected with the at least one controller/data processor 102 is
the EOR database 1B. The data processor 102 is also connected with
interfaces/adapters 108 that are configured to receive data from
the various source inputs S.sub.1, S.sub.n, S.sub.N. Also connected
with the at least one controller/data processor 102 is at least one
display device/GUI 110 that implements at least in part the various
simulation visualization operations (e.g., blocks 1G, 1L) as well
as the EOR efficiency prediction block 1M.
[0107] In general the various components and sub-systems shown in
FIG. 8 can be implemented in whole or in part as circuitry and/or
as separate special purpose data processor/controllers and/or as
the software 106.
[0108] The simulator 10 can be physically instantiated in whole or
in part as one or more computers and computing systems at an
enterprise, such as at a natural resources exploration/recovery
enterprise, or it could be, for example, instantiated at an agency
or an academic institution, or it can be instantiated in whole or
in part in a virtual manner in the cloud.
[0109] In some embodiments the use of the simulator 10 can be
provided as a service to researchers and others via data
communication networks including the Internet.
[0110] In whatever physical/virtual form the simulator 10 is
instantiated it can be assumed to include certain cooperating
functionality that is responsive to the input source/sensor data
(source inputs S.sub.1, S.sub.n, S.sub.N), as well as to the other
input and/or calculated data stored in the EOR database 1B, to
execute whatever modeling/simulation programs that are selected by
the user at least for the purpose of determining optimum additives
and corresponding EOR efficiencies for some natural
resource-containing reservoir(s). This cooperative functionality
can include, in addition to the EOR database 1B, some or all of the
various blocks 1A and 1C-1M which can be realized as physical
components/circuitry and/or as executable program code modules and
partitions.
[0111] The present invention may be a system, a method, and/or a
computer program product. The computer program product may include
a computer readable storage medium (or media) having computer
readable program instructions thereon for causing a processor to
carry out aspects of the present invention.
[0112] FIG. 9 is a logic flow diagram for capillary network
simulations based on a low-dimensional representation of porous
media, and illustrates the operation of an exemplary method, a
result of execution of computer program instructions embodied on a
computer readable memory, functions performed by logic implemented
in hardware, and/or interconnected means for performing functions
in accordance with exemplary embodiments.
[0113] Referring to FIG. 9, a method may be provided including:
receiving data corresponding to a three-dimensional physical
representation of a porous rock sample as indicated by block 900;
calculating a low-dimensional representation of a pore network in
the porous rock sample based on the three-dimensional physical
representation as indicated by block 902; extracting one or more
geometrical parameter from the low-dimension representation as
indicated by block 904; generating a capillary network model of the
porous rock sample based at least on the at least one geometrical
parameter for simulating fluid flow inside the porous rock sample
as indicated by block 906; and performing at least one simulation
of a flow of fluid through the capillary network model of the
porous rock sample with a fluid additive to provide a predicted
enhanced fluid recovery efficiency as indicated by block 908.
[0114] The low-dimensional representation of the pore network may
be a centerline representation that comprises a set of centerlines
representing the pore network. The centerline representation may be
indicative of a spatial variation of a diameter, tortuosity,
geometry and connectivity of the pore network. Extracting the at
least one geometrical parameter may include generating a first list
of values for each centerline in the set, the first list comprising
values for at least one of the following centerline parameters: a
centerline diameter, a centerline length, centerline endpoints;
centerline direction; centerline azimuthal angle; centerline
tortuosity; centerline curvature; and centerline torsion.
Extracting the at least one geometrical parameter further may
include generating a second list of values defined for each pair of
connected centerlines in the set of centerlines, the second list
comprising values for at least one of the following centerline
parameters: an angle between each pair of connected centerlines:
and a diameter variation between each pair of connected
centerlines. Extracting the at least one geometrical parameter may
include calculating for the set of centerlines at least one of: a
total number of nodes at which centerlines in the set connect to
each other; a total number of centerlines that are connected to an
inlet and/or an outlet of a given centerline in the set; a binary
matrix depicting connections between centerlines in the set;
statistics corresponding to the generated first lists and the
generated second lists; and two-dimensional plots relating every
parameter in each of the first lists to every parameter in the
second list . Performing at least one simulation of capillary model
may include at least one of: determining a simulation type
comprising at least one of a probabilistic simulation type that is
time-independent, and a dynamic simulation type that is
time-dependent; determining a flow regime where either inertial and
kinetic forces are ignored in the at least one simulation or
inertial and kinetic forces are considered in the at least one
simulation; and determining an interface type from a plurality of
interface types, wherein the plurality of interface types comprises
at least one multi-phase interface type. The interface type may be
selected based on one or more of: wetting properties of the porous
rock sample; initial position of the fluid and initial fluxes,
inlet and/or outlet pressures, flow rates, and external forces; and
rheology properties and surface tension of the fluid. The interface
type may be selected by a user via a user input.
[0115] According to another embodiment, an apparatus (e.g.
simulator 10 of FIG. 8) may be provided, comprising at least one
processor; and at least one memory including computer program code,
the at least one memory and the computer program code configured
to, with the at least one processor, cause the apparatus to at
least: receive data corresponding to a three-dimensional physical
representation of a porous rock sample; calculate a low-dimensional
representation of a pore network in the porous rock sample based on
the three-dimensional physical representation; extract one or more
geometrical parameter from the low-dimension representation;
generate a capillary network model of the porous rock sample based
at least on the at least one geometrical parameter for simulating
fluid flow inside the porous rock sample; and perform at least one
simulation of a flow of fluid through the capillary network model
of the porous rock sample with a fluid additive to provide a
predicted enhanced fluid recovery efficiency.
[0116] The low-dimensional representation of the pore network may
be a centerline representation that comprises a set of centerlines
representing the pore network. The centerline representation may be
indicative of a spatial variation of a diameter, tortuosity,
geometry and connectivity of the pore network. Extraction of the at
least one geometrical parameter may include generating a first list
of values for each centerline in the set, the first list comprising
values for at least one of the following centerline parameters: a
centerline diameter, a centerline length, centerline endpoints;
centerline direction; centerline azimuthal angle; centerline
tortuosity; centerline curvature; and centerline torsion. The
extraction of the at least one geometrical parameter may include
generating a second list of values defined for each pair of
connected centerlines in the set of centerlines, the second list
comprising values for at least one of the following centerline
parameters: an angle between each pair of connected centerlines:
and a diameter variation between each pair of connected
centerlines. The extraction of the at least one geometrical
parameter may include calculating for the set of centerlines at
least one of: a total number of nodes at which centerlines in the
set connect to each other; a total number of centerlines that are
connected to an inlet and/or an outlet of a given centerline in the
set; a binary matrix depicting connections between centerlines in
the set; statistics corresponding to the generated first lists and
the generated second lists; and two-dimensional plots relating
every parameter in each of the first lists to every parameter in
the second list. Performance of the at least one simulation of
capillary model may include at least one of: determination of a
simulation type comprising at least one of a probabilistic
simulation type that is time-independent, and a dynamic simulation
type that is time-dependent; determination of a flow regime where
either inertial and kinetic forces are ignored in the at least one
simulation or inertial and kinetic forces are considered in the at
least one simulation; and determination of an interface type from a
plurality of interface types, wherein the plurality of interface
types comprises at least one multi-phase interface type. The
interface type may be selected based on one or more of: wetting
properties of the porous rock sample; initial position of the fluid
and initial fluxes, inlet and/or outlet pressures, flow rates, and
external forces; and rheology properties and surface tension of the
fluid. The interface type is selected by a user via a user
input.
[0117] According to another embodiment, a computer program product
for capillary network simulations, the computer program product
comprising a computer readable storage medium (e.g. memory 104 of
FIG. 8) having program instructions embodied therewith, the program
instructions executable by a device to cause the device to: receive
data corresponding to a three-dimensional physical representation
of a porous rock sample; calculate a low-dimensional representation
of a pore network in the porous rock sample based on the
three-dimensional physical representation; extract one or more
geometrical parameter from the low-dimension representation;
generate a capillary network model of the porous rock sample based
at least on the at least one geometrical parameter for simulating
fluid flow inside the porous rock sample; perform at least one
simulation of a flow of fluid through the capillary network model
of the porous rock sample with a fluid additive to provide a
predicted enhanced fluid recovery efficiency.
[0118] The low-dimensional representation of the pore network is a
centerline representation that comprises a set of centerlines
representing the pore network, and wherein the centerline
representation is indicative of a spatial variation of a diameter,
tortuosity, geometry and connectivity of the pore network.
[0119] The computer readable storage medium can be a tangible
device that can retain and store instructions for use by an
instruction execution device. The computer readable storage medium
may be, for example, but is not limited to, an electronic storage
device, a magnetic storage device, an optical storage device, an
electromagnetic storage device, a semiconductor storage device, or
any suitable combination of the foregoing. A non-exhaustive list of
more specific examples of the computer readable storage medium
includes the following: a portable computer diskette, a hard disk,
a random access memory (RAM), a read-only memory (ROM), an erasable
programmable read-only memory (EPROM or Flash memory), a static
random access memory (SRAM), a portable compact disc read-only
memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a
floppy disk, a mechanically encoded device such as punch-cards or
raised structures in a groove having instructions recorded thereon,
and any suitable combination of the foregoing. A computer readable
storage medium, as used herein, is not to be construed as being
transitory signals per se, such as radio waves or other freely
propagating electromagnetic waves, electromagnetic waves
propagating through a waveguide or other transmission media (e.g.,
light pulses passing through a fiber-optic cable), or electrical
signals transmitted through a wire.
[0120] Computer readable program instructions described herein can
be downloaded to respective computing/processing devices from a
computer readable storage medium or to an external computer or
external storage device via a network, for example, the Internet, a
local area network, a wide area network and/or a wireless network.
The network may comprise copper transmission cables, optical
transmission fibers, wireless transmission, routers, firewalls,
switches, gateway computers and/or edge servers. A network adapter
card or network interface in each computing/processing device
receives computer readable program instructions from the network
and forwards the computer readable program instructions for storage
in a computer readable storage medium within the respective
computing/processing device.
[0121] Computer readable program instructions for carrying out
operations of the present invention may be assembler instructions,
instruction-set-architecture (ISA) instructions, machine
instructions, machine dependent instructions, microcode, firmware
instructions, state-setting data, configuration data for integrated
circuitry, or either source code or object code written in any
combination of one or more programming languages, including an
object oriented programming language such as Smalltalk, C++, or the
like, and procedural programming languages, such as the "C"
programming language or similar programming languages. The computer
readable program instructions may execute entirely on the user's
computer, partly on the user's computer, as a stand-alone software
package, partly on the user's computer and partly on a remote
computer or entirely on the remote computer or server. In the
latter scenario, the remote computer may be connected to the user's
computer through any type of network, including a local area
network (LAN) or a wide area network (WAN), or the connection may
be made to an external computer (for example, through the Internet
using an Internet Service Provider). In some embodiments,
electronic circuitry including, for example, programmable logic
circuitry, field-programmable gate arrays (FPGA), or programmable
logic arrays (PLA) may execute the computer readable program
instructions by utilizing state information of the computer
readable program instructions to personalize the electronic
circuitry, in order to perform aspects of the present
invention.
[0122] Aspects of the present invention are described herein with
reference to flowchart illustrations and/or block diagrams of
methods, apparatus (systems), and computer program products
according to embodiments of the invention. It will be understood
that each block of the flowchart illustrations and/or block
diagrams, and combinations of blocks in the flowchart illustrations
and/or block diagrams, can be implemented by computer readable
program instructions.
[0123] These computer readable program instructions may be provided
to a processor of a general purpose computer, special purpose
computer, or other programmable data processing apparatus to
produce a machine, such that the instructions, which execute via
the processor of the computer or other programmable data processing
apparatus, create means for implementing the functions/acts
specified in the flowchart and/or block diagram block or blocks.
These computer readable program instructions may also be stored in
a computer readable storage medium that can direct a computer, a
programmable data processing apparatus, and/or other devices to
function in a particular manner, such that the computer readable
storage medium having instructions stored therein comprises an
article of manufacture including instructions which implement
aspects of the function/act specified in the flowchart and/or block
diagram block or blocks.
[0124] The computer readable program instructions may also be
loaded onto a computer, other programmable data processing
apparatus, or other device to cause a series of operational steps
to be performed on the computer, other programmable apparatus or
other device to produce a computer implemented process, such that
the instructions which execute on the computer, other programmable
apparatus, or other device implement the functions/acts specified
in the flowchart and/or block diagram block or blocks.
[0125] The flowchart and block diagrams in the Figures illustrate
the architecture, functionality, and operation of possible
implementations of systems, methods, and computer program products
according to various embodiments of the present invention. In this
regard, each block in the flowchart or block diagrams may represent
a module, segment, or portion of instructions, which comprises one
or more executable instructions for implementing the specified
logical function(s). In some alternative implementations, the
functions noted in the blocks may occur out of the order noted in
the Figures. For example, two blocks shown in succession may, in
fact, be executed substantially concurrently, or the blocks may
sometimes be executed in the reverse order, depending upon the
functionality involved. It will also be noted that each block of
the block diagrams and/or flowchart illustration, and combinations
of blocks in the block diagrams and/or flowchart illustration, can
be implemented by special purpose hardware-based systems that
perform the specified functions or acts or carry out combinations
of special purpose hardware and computer instructions.
* * * * *
References